If they say the thyroid is fine, I've had really good results with the approach of 'oh, my dogs used to be fat and they didn't even eat that much, and then I found out the food I was feeding was full of stuff like corn and wheat!' (Okay, my dogs were NEVER nearly that fat, but I will lie through my teeth to make a point.)
As much as people don't like to be lectured about how they are caring for their animals, they do love to share problems and swap suggestions for solutions. I try to take that line whenever possible. And I guarantee you, the owners of that dog know it's fat and they know that's not good. I suspect they just don't know how to address the problem, the dog probably begs food from them with great success, and I would bet too that they're feeding a really sub-par food. And that they think a more expensive food is just a waste of money because the dog will eat the same amount of it.
If you can walk them through those points, Amanda (and I know you can
), I bet you'll help that dog out a lot.